Two topics related to the general field of free energy conversion in biology have been studied and gained great progress. First, we continued our study of the general dynamic properties of a Brownian particle in a fluctuating periodic potential. We have obtained a general formalism for this Brownian motion system, which can be used to calculate the velocity of the movement of a large bead on a periodic biopolymer (such as a microtubule) powered by a one-headed motor molecule (such as kinesin), as measured in in vitro experiments. The formalism can also be used to design or set up devices for the separation of proteins or small particles based their sizes and charges, etc.. Specifically, we have found that charged particles with different charges or different diffusion coefficients can be made to move in opposite directions in a fluctuating linear periodic potential. Thus, particle separation should be more efficient based on this principle than on other conventional methods, such as the electrophoresis. The second topic is related to the regulation of muscle contraction (the mechano-chemical free energy conversion system). Specifically, we were interested in the question of how the regulatory protein, caldesmon, found on smooth muscles controls the generation of the force between the myosin head (the cross-bridge)and the actin, responsible for muscle contraction. In general, caldesmon molecules can reduce the force generation by reducing the ATP hydrolysis rate or by reducing the number of binding sites on actin for myosin heads. Using equilibrium binding data measured for the simultaneous binding of myosin and caldesmon molecules to actin, we have concluded that there are at least two modes of simultaneous binding of myosin and caldesmon to actin: the pure competitive and the mosaic multiple binding. In this study, we have developed a kinetic Monte Carlo method to differentiate this two binding models. When applied to the kinetic data measured by Dr. Chalovich and his colleagues (at University of East North Carolina), we have found that the binding of myosin and caldesmon to actins without tropomyosin is more like pure competitive. On the other hand, the binding to actins with tropomyosins (a condition in real muscle) can be fitted with both models. The method can be extended to binding models involving more than two ligands and should be useful in delineating different modes of regulation of different regulatory proteins in a complex system (e.g., such as in a protein transcription complex).